We present a novel adaptive oscillator, called Adaptive Natural Oscillator (ANO), to exploit the natural dynamics of a given robotic system. This tool is built upon the Adaptive Frequency Oscillator (AFO), and it can be used as a pattern generator in robotic applications such as locomotion systems. In contrast to AFO, that adapts to the frequency of an external signal, ANO adapts the frequency of reference trajectory to the natural dynamics of the given system. In this work, we prove that, in linear systems, ANO converges to the system's natural frequency. Furthermore, we show that this tool exploits the natural dynamics for energy efficiency through minimization of actuator effort. This property makes ANO an appealing tool for energy consumption reduction in cyclic tasks; especially in legged systems. We also extend the proposed adaptation mechanism to high dimensional and general cases; such as n-DOF manipulators. In addition, by investigating a hopper leg in simulation, we show the efficacy of ANO in face of dynamical discontinuities; such as those inherent in legged locomotion. Furthermore, we apply ANO to a simulated compliant robotic manipulator performing a periodic task where the energy consumption is drastically reduced. Finally, the experimental results on a 1-DOF compliant joint show that our adaptive oscillator, despite all practical uncertainties and deviations from theoretical models, exploits the natural dynamics and reduces the energy consumption.